# Geometric Optimization of Restricted-Open and Complete Active Space Self-Consistent Field Wavefunctions

arXiv: https://arxiv.org/abs/2404.14655 · HTML: https://mlsanity.com/paper/2404.14655/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Apr 2024.

## Built on by (most cited first, 1 of 1)

- [Nested subspace learning with flags](https://mlsanity.com/paper/2502.06022/) (2025)

## Abstract (arXiv)

We explore Riemannian optimization methods for Restricted-Open-shell Hartree-Fock (ROHF) and Complete Active Space Self-Consistent Field (CASSCF) methods. After showing that ROHF and CASSCF can be reformulated as optimization problems on so-called flag manifolds, we review Riemannian optimization basics and their application to these specific problems. We compare these methods to traditional ones and find robust convergence properties without fine-tuning of numerical parameters. Our study suggests Riemannian optimization as a valuable addition to orbital optimization for ROHF and CASSCF, warranting further investigation.